Permutation/Sign via transpositions/Fact

Let ${\displaystyle {}M=\{1,\ldots ,n\}}$ and let ${\displaystyle {}\pi }$ be a permutation on ${\displaystyle {}M}$. Let

${\displaystyle {}\pi =\tau _{1}\cdots \tau _{r}\,}$

be written as a product of ${\displaystyle {}r}$ transpositions.